If the trip materializes, he is expected to hold discussions with Prime Minister Nguyen Xuan Phuc, Japanese news agency Kyodo News reported on Wednesday, citing government sources.
Japan seeks to strengthen ties with ASEAN member countries amid growing tensions between the U.S. and China over trade, security and other issues, it said.
Vietnam is the ASEAN chair this year.
Japanese national broadcaster NHK said a decision would be made after assessing the Covid-19 situation in both countries.
The Japanese PM also intends to visit Indonesia in October to hold talks with President Joko Widodo.
Suga, 71, became prime minister after winning a parliamentary vote, taking over from Shinzo Abe, who resigned over health issues along with his cabinet.
He was considered Abe’s right hand, serving as chief cabinet secretary for eight years.
Vietnam recently approved the resumption of commercial flights to seven Asian destinations: mainland China, Japan, South Korea, Taiwan, Laos, Cambodia, and Thailand.
A flight from Hanoi to Tokyo, Vietnam's first international commercial flight in months, took off September 19.
Vietnam has had no local transmission for nearly a month.